Although he is the party’s most recent president and has been out of the White House for only three years, George W. Bush is rarely invoked by candidates, speakers or GOP voters. They seek to think of him as the Invisible Man — if they think of him at all.

At campaign stops, Newt Gingrich regularly heaps praise on Ronald Reagan. The Bush years have been barely mentioned during the presidential debates. Rick Santorum, at town halls Thursday, made a passing reference to Bush on domestic and foreign policy, but not in a complimentary way.

Asked why the former president’s name is so rarely mentioned, few Granite State Republicans seem eager to embrace the Texan’s legacy of budget deficits, billion-dollar wars and domestic policies that didn’t pass muster with conservatives.

“He lost me on illegal immigration,” said Bob Grover, a 61-year-old unemployed carpenter from Northfield. He voted twice for Bush but says: “Do I think he was a great president? No.”

At a Santorum town hall meeting at an old train station in Northfield, Republican Roger Iliff was even more blunt.

“When we started that war in Iraq, it just didn’t seem right,” said Iliff, a 71-year-old retired aircraft mechanic. “When we didn’t find the weapons of mass destruction, it made the whole government look like a bunch of dopes. And he was the leader.”

That’s not to say Republicans gathering in cafes, public libraries and fire stations in advance of Tuesday’s GOP primary don’t believe that Democrat Barack Obama is to blame for making a mess of things. It’s just that they don’t believe Bush is the model to fix them.

Bush has largely stayed out of the limelight since leaving office. He has declined to inject himself into the presidential race, and while members of his family have endorsed candidates, he has not.

Bush lost the New Hampshire primary in 2000, and to Yankee sensibilities, the memory of Bush bears a certain Southern, cowboy patina — and not in a good way. “They made fun of him,” said Albert Hansen, a 70-year-old former shipbuilder.

Still, New Hampshire is not the only state where Bush goes largely unmentioned. The government spending, growing debt and economic collapse that attended Bush’s departure is not exactly something Republican candidates want to talk about — except to say that Obama has made matters worse.

The candidate most likely to invoke Bush’s name has been Rick Perry. Four years ago, he told an Iowa audience while campaigning for Rudy Giuliani that Bush had “never, ever been a fiscal conservative.” This year, Perry has blamed both Bush-era Republicans and Obama-era Democrats for the problems bedeviling Washington.

Otherwise, presidential candidates have tended to treat Bush as the man who wasn’t there — except when helpful to mention that he was.

After Santorum went on at length Thursday about Obama’s foreign-policy failures, a questioner at the town hall in Northfield pointed out that the president got Osama bin Laden.

“That was a continuation of the policy put in place by the Bush administration,” Santorum said.